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We study in detail the viability and the patterns of a strong first-orderelectroweak phase transition as a prerequisite to electroweak baryogenesis inthe framework of $Z_3$-invariant Next-to-Minimal Supersymmetric Standard Model(NMSSM), in the light of recent experimental results from the Higgs sector,dark matter (DM) searches and those from the searches of the lighter charginoand neutralinos at the Large Hadron Collider (LHC). For the latter, weundertake thorough recasts of the relevant, recent LHC analyses. With the helpof a few benchmark scenarios, we demonstrate that while the LHC has started toeliminate regions of the parameter space with relatively small$\mu_\mathrm{eff}$, that favors the coveted strong first-order phasetransition, rather steadily, there remains phenomenologically much involved andcompatible regions of the same which are yet not sensitive to the current LHCanalyses. It is further noted that such a region could also be compatible withall pertinent theoretical and experimental constraints. We then proceed toanalyze the prospects of detecting the stochastic gravitational waves, whichare expected to arise from such a phase transition, at various future/proposedexperiments, within the mentioned theoretical framework and find them to besomewhat ambitious under the currently projected sensitivities of thoseexperiments.

the journal of high energy physics/the journal of high energy physics

Electroweak Phase Transition in the $Z_3$-invariant NMSSM: Implications  of LHC and Dark matter searches and prospects of detecting the gravitational  waves